There's a $1.75 million buyout for 2016 and a $250,000 buyout for 2017.
"This has all swept me off my feet," Luebke told reporters Friday. "They made a pretty fair offer. They got through it pretty quick. [The contract] wasn't something I wanted to think about when I was pitching."
Byrnes and Luebke's agent, Barry Meister, worked face-to-face on the deal in Arizona on Wednesday and Thursday.
Luebke, who turned 27 on March 4, was 6-10 overall with a 3.29 ERA in 139 2/3 innings last season. He started the season as a long reliever before moving into the starting rotation.
Luebke will likely slot behind Tim Stauffer as the No. 2 pitcher in the rotation this season.
Earlier this month, the Padres agreed to similar contract extensions with outfielder Cameron Maybin and catcher Nick Hundley. The team has committed a combined $46 million to the three players.
"These guys we view as core players," said Padres general manager Josh Byrnes.
All three deals were signed off on by majority owner John Moores.
Luebke allowed 105 hits in 139 2/3 innings, which is something managers and pitching coaches always look at -- a low hits-to-innings-pitched ratio. There were the 154 strikeouts he had over that period of time -- meaning that Luebke missed a lot of bats. He also showed good command (44 walks).
"He's got good stuff and he's got an assortment of pitches now that he can feel confident in to keep him progressing," Padres manager Bud Black said recently.
Pitching coach Darren Balsley has raved this spring about Luebke and his potential.
"The size, his athletic ability, his intellect," Balsley said recently. "When he puts it together -- and I'm not going to say if -- he's going to be one of the more dominant lefties in the National League."
The Padres have asked Luebke to add a changeup this spring and he's embraced the pitch to the point where he's throwing it a handful of times in games, even when he's behind in the count.
"He's been a little of a late bloomer," Byrnes said. "He did well in the bullpen and adapted well to the rotation. He's a guy who seems to be getting better and better. As good as 2011 [was], we feel he has more weapons now."
Luebke, who was the 67th overall pick in the 2007 First-Year Player Draft out of Ohio State, said he was humbled by the contract.
"I've had great guys to learn from," Luebke said of Black and Balsley. "I really love the city and they've treated me well since the day I was drafted. I'm going to try to do something to get better each day."